随机复合材料结构非线性热-力耦合模拟的统计高阶多尺度方法

对于具有复杂随机细观构造的复合材料结构的非线性热-力耦合问题的随机多尺度建模和计算仍是一个具有挑战性的问题。本文发展了一个新的统计高阶多尺度方法，克服了随机多尺度问题直接模拟时巨大的计算量，实现了具有随机复合材料结构非线性热-力耦合问题的数值模拟。借助统计多尺度渐近分析和泰勒级数方法，本文严格推导了可以精确分析随机复合材料结构宏-细观尺度非线性热-力耦合响应的统计高阶多尺度计算模型。然后，通过局部误差分析证明了统计高阶多尺度计算模型中高阶校正项在保持计算模型局部能量和动量守恒的重要意义。进一步，建立了可以高效模拟随机复合材料结构非线性热-力耦合行为的具有离线和在线两阶段的时空多尺度算法。最后，通过数值实验验证了统计高阶多尺度方法的计算高效率和高精度。

Statistical higher-order multi-scale method for nonlinear thermo-mechanical simulation of composite structures with periodically random configurations

Stochastic multi-scale modeling and simulation for nonlinear thermo-mechanical problems of composite structures with complicated random microstructures remains a challenging issue.In this paper, we develop a novel statistical higher-order multi-scale (SHOMS) method for nonlinear thermo-mechanical simulation of composite structures with periodically random configurations, which is designed to overcome limitations of prohibitive computation involving the macro-scale and micro-scale.By virtue of statistical multi-scale asymptotic analysis and Taylor series method, the SHOMS computational model is rigorously derived for accurately analyzing nonlinear thermo-mechanical responses of random composite structures both in the macro-scale and micro-scale.Moreover, the local error analysis of SHOMS solutions in the point-wise sense clearly illustrates the crucial indispensability of establishing the higher-order asymptotic corrected terms in SHOMS computational model for keeping the conservation of local energy and momentum.Then, the corresponding space-time multi-scale numerical algorithm with off-line and on-line stages is designed to efficiently simulate nonlinear thermo-mechanical behaviors of random composite structures.Finally, extensive numerical experiments are presented to gauge the efficiency and accuracy of the proposed SHOMS approach.